On topological and Hodge theoretic invariants of curves and families of curves
Bibliographic record
Abstract
In this thesis, we study topological and Hodge theoretic invariants associated to smooth complex algebraic varieties with particular focuses on algebraic curves and smooth projective families of curves. The central question we would like to understand is to what extent these invariants capture morphisms between the corresponding varieties. More precisely, inspired by Grothendieck's section conjecture in anabelian geometry, we formulated and studied a topological and a Hodge theoretic section question for smooth projective family of curves and made progress towards answering those questions. In the topological setting, many of our results are analogous to existing results in anabelian geometry. In the Hodge setting, much less is known, and so we also studied the connection between the Hodge theoretic section question and classical results in non-abelian Hodge theory. In a different direction, motivated by the famous theorem of Torelli, we studied if the Torelli's theorem can be made functorial. We construct interesting examples of morphisms of Hodge structures which do not arise from morphism between curves, and connect our construction to the study of isotrivial isogeny factors in family of curves.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".